Iterative Methods for Systems of Equations

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Typical Scheduling: 
Every spring (MATH) and fall (CSE)

Iterative methods for linear and nonlinear systems of equations including Jacobi, G-S, SOR, CG, multigrid, fixed point methods, Newton quasi-Newton, updating, gradient methods. Crosslisted with CSE 6644.


MATH 2406 or MATH 4305 or consent of School

Course Text: 

Iterative Methods for Linear and Nonlinear Equations by C.T. Kelley - ISBN 978-0898713527 (SIAM)
Iterative Methods for Solving Linear Systems by Anne Greenbaum - ISBN 978-0898713961 (SIAM)

Topic Outline: 
  • Review of Iterative Methods for Linear Systems - Gauss-Jacobi, Gauss-Seidel, SOR, convergence, implementation storage of sparse matrices, discretization of elliptic problems
  • Modern Iterative Methods for Linear Systems - Krylov subspace methods: conjugate gradient, GMRES, QMR, multigrid methods, domain decomposition, preconditioning
  • Nonlinear Problems - Unconstrained optimization, differential equations, bifurcation problems
  • Review of Fixed Point Methods - Fixed point iteration, convergence
  • Newton's Method - Local convergence, Kantorovich theory, implementation, termination, inexact Newton's methods
  • Globally Convergent Methods - Quasi-Newton methods, line searches, model-trust region approach, convergence
  • Secant Methods - Broyden's method, updates, implementation with quasi-Newton methods, convergence
  • Specific Applications According to the Instructor's Interests